You rely on your visual cortex, located at the back of your brain, to process the images that you see. When light enters your eye, it stimulates certain parts in the visual cortex, forming a pattern of excited neurons, which you experience as an image. But once in a while, these excitation patterns arise spontaneously, overwhelming the visual signal from the eyes and causing geometric hallucinations. This "failure mode" only occurs when some influence, such as drugs, compromises your normal brain function.

The pattern of neurons that makes you visualize things that aren't there arises because of a type of self-organizing diffusion called the Turing mechanism, which contributes to the creation of patterns in certain biological and ecological systems.

As author Nigel Goldenfeld describes the mechanism:

"Normally we think of diffusion as a process which smooths things out. Think of an unequal density distribution in a gas. As the atoms diffuse around eventually the density becomes uniform. When you have diffusion occurring with nonlinear chemical reactions, however, the opposite happens. The chemical species separate and form domains of differing chemical composition. This was Alan Turing's surprising discovery."

These "Turing patterns" form in reaction-diffusion systems that contain two competing forces: an activator, and an inhibitor. For example, in a predator-prey ecological system, the prey are the activators, trying to reproduce, while the predators act as inhibitors, slowing the activators' rate of production. Goldenfeld says,

"Another system where Turing patterns arise is ecology. Instead of chemical reactions, you have interactions between species: for example, creature A eats creature B. If you take into account birth and death, predator competition, and the fact that birth rate depends on species density (if you ever had a long distance relationship, you'll understand where this comes from), you find that the equations governing the spatial and temporal distributions of species are the same as those describing chemical reactions. So you can get patterns of high and low species abundance. "

In the brain, the firing of a neuron can either encourage or prevent the firing of its connected neighbors, which means that neurons can act as both activators and inhibitors, making Turing patterns possible. In fact, the researchers suggest that if the visual cortex had a slightly different structure, the Turing mechanism would produce spontaneous neural patterns in it all the time, leading to permanent hallucinations. While this might be fun, it would barely let us see our surroundings. "There would be strong selection pressure against people who think they are seeing weird spiral patterns when in fact what is in front of their face is a hungry tiger!" explains Goldenfeld.

Instead, the researchers posit that the topology of the visual cortex does not allow the "inhibitor" signals to travel long distances, which is a requirement for the Turing mechanism. This prevents the Turing mechanism from working properly, giving neurons uniform diffusion patterns rather than geometric Turing patterns. Without the Turing mechanism to create interfering neural excitation patterns, the dominant patterns will be based on external stimuli: namely, normal visual signals from the eyes.

To test this hypothesis, the researchers created two models, one based on the actual structure of the visual cortex, the other a "physiologically plausible alternative network." The authors - who include Thomas Charles Butler, Marc Benayoun, Edward Wallace, Wim van Drongelen, and Jack Cowan, in addition to Goldenfeld - write,

When you take psychotropic drugs, disrupting your brain's normal activity, you may see geometric hallucinations like the image at left, which arose out of the alternative network. If your brain was normally structured like this, you might see a geometric pattern overlaying your vision at all times.

In the model of the real visual cortex, on the other hand, the Turing mechanism smoothes out, creating this even, uniform pattern, which could easily be overwritten by visual input. It would have been physically possible for the visual cortex to have developed into the structure of the alternative network. But natural selection prefers unclouded eyesight, evolving a visual cortex with the necessary constraints to prevent round-the-clock hallucinations… unless, of course, you've taken something to cause them.